THE EXISTENCE AND ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS WITH AN INTERIOR LAYER OF BURGERS TYPE EQUATIONS WITH MODULAR ADVECTION

We consider a new class of singularly perturbed parabolic periodic boundary value problems for reaction-advection-diffusion equations: Burgers type equations with modular advection. We construct the interior layer type formal asymptotics and propose a modified procedure to get asymptotic lower and upper solutions. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution with an interior layer and estimate the accuracy of its asymptotics. The asymptotic stability of this solution is also established.